Magnetic spheres in microwave cavities

We apply Mie scattering theory to study the interaction of magnetic spheres with microwaves in cavities beyond the magnetostatic and rotating wave approximations. We demonstrate that both strong and ultra-strong coupling can be realized for a stand alone magnetic spheres made from yttrium iron garnet (YIG), acting as an efficient microwave antenna. The eigenmodes of YIG spheres with radii of the order mm's display distinct higher angular momentum character that has been observed in experiments.